Assume that the number of defects in a car has a Poisson distribution with parameter l. To estimate l we obtain the random sample X1, X2, . . ., Xn. a. Find the Fisher information in a single observation using two methods.
b. Find the Cramer–Rao lower bound for the variance of an unbiased estimator of h.
c. Use the score function to find the mle of h and show that the mle is an efficient estimator.
d. Is the asymptotic distribution of the mle in accord with the second theorem? Explain.